University of Illinois at Urbana-Champaign
College of Liberal Arts and Sciences
Department of Mathematics

Mathematics 120, section E
Calculus and Analytic Geometry, I
1-1:50 PM MWF
314 Altgeld Hall

Professor Daniel R. Grayson
Office: 357 Altgeld Hall
Phone: 3-6209

Quick links:

  • Email me
  • The newsgroup. For off-campus use of the newsgroup, click here to get a password emailed to you, and then click here to use the newsgroup with that password.
  • Score reports.
  • Publisher's student resources.
  • The Calculus Page
  • Lecture notes:
  • September 12: page 1 page 2 page 3 page 4.
  • September 14: page 1 page 2 page 3 page 3b page 4 page 5.
  • Introduction:

    For those of you who are new on campus, welcome to the University and to college life! You have a straight A average so far at the University of Illinois, and I will try to help you keep it that way. For the rest of you, welcome back!

    You can succeed in calculus, even though it is harder than the math courses you have had in high school. It might be twice as hard! Here is what you have to do.

  • Read, study, and think about the book.
  • Attend the lectures on Monday, Wednesday, and Friday.
  • Attend the discussion sessions on Tuesday and Thursday, during which quizzes are given..
  • Do the homework regularly.
  • Form a study group -- meet weekly, prepare a homework assignment, and then discuss your solutions in the group. (Discussing the solutions is fine, but don't copy them -- you are expected to write up your own homework.)
  • Get help from the discussion leaders for problems you can't do.
  • Use the newsgroup to get help.
  • Identify the things you don't understand and get help on them.
  • Don't let your work for this course slide for even a week.
  • You should study the book carefully and learn from it outside of class. It is well written and will reward close study. Plan on allotting at least an hour per day for this, starting from the first day. We love to answer questions about the material in the book, so if there is a sentence or paragraph that doesn't make sense to you, let us know (hopefully, using the news group) so we can help you out.

    The main thing is to start today! At the pace things happen in college, you don't want to procrastinate for even a week.

    Goal of the course:

    The chief difference between calculus and high school geometry is that we take the passage of time into account and use it as a tool. For example, we might try to measure the volume of a sphere by letting its radius shrink to zero and recording the rate at which the volume dissipates.

    The fundamental laws of physics that govern the world tend to be expressed as differential equations. These equations encapsulate information about how each little bit of matter interacts with each other little bit. One of the applications of calculus is to pass from the fundamental laws to explicit formulas for the global behavior of particular systems.

    In this course we take the first step toward understanding the role mathematics has to play in coordinating the basic laws of nature by learning about differentiation and integration of functions.


    The textbook is "Calculus: Early Transcendentals", by Stewart, Fourth Edition. It's available in the book stores.


    Lectures take place on Monday, Wednesday, and Friday at 1PM in 314 Altgeld Hall. In the lectures we will present to you the basic concepts and tools which you will need for learning the material and attacking the problems.

    Discussion leaders:

    Discussion sections take place on Tuesday and Thursday at 1 (the R sections) or 2 PM (the S sections). They have a maximum enrollment of 35, so this is the place where you can get practical help in executing the algorithms explained in lecture, and you can get answers to your questions about the material in the book or homework. Prepare for discussion by reading the material, reviewing your notes from lecture, and doing the homework.

    The discussion leaders will have office hours, mark your homework, grade your quizzes, and spend time looking at the news group to answer questions that appear there. You are welcome to go to the office hours of any of the discussion leaders.

  • Joyce Chau, section R1, email, home page, office hours Tuesdays 3-5, in room B1 Coble Hall.
  • Vandana Venkat, sections R2 and S2, email, home page, office hours Mondays and Wednesdays 3:30-5, in room B1 Coble Hall.
  • Tyler Alumbaugh, section R3, email, home page, office hours Tuesdays 3-4, Wednesdays 2-3, in room B1 Coble Hall.
  • Malgorzata Konwerska, section S1, email, home page, office hours Tuesdays 3-4, and Wednesdays 2-3, in room B1 Coble Hall.
  • Xiaodong Li, section WE1, email, home page, office hours Tuesday 2-3 and Wednesday 3-4, in room B1 Coble Hall.
  • Our newsgroup:

    The professor, teaching assistants, and other students will be able to see the newsgroup, and we will monitor the news group and try to answer your questions promptly.

    If you are using a browser as a newsreader, you will want to tell it who you are, so the messages you post will be identified. For example, in Netscape, select "Preferences" from the "Edit" menu, and then under "Mail & Newsgroups" select "Identity".

    Don't be embarrassed about not knowing the answer to a problem. Just post your question and get the help you need to succeed!

    Learn how to post articles to the news group. There are two ways, depending on whether you want to follow up on a topic in a message previously posted, or to initiate a new topic of discussion. If your followups are posted as such, it makes it a lot easier for readers of the news group to follow the various threads of discussion.

    Here is a primitive but serviceable way to include mathematical formulas in email messages and articles in the news group. Use a caret (^) to indicate exponentiation, an underscore (_) to indicate a subscript, and an asterisk (*) to indicate multiplication. Thus "x^2" would mean "x squared", "x_3" would mean "x sub 3", and "x*y" would mean "x times y". Never use "x" as a "times" sign. Some formulas can often be rendered in a 2-dimensional form that looks like this:

                   2     2
            (x + 2)  =  x  + 4 x + 4
            dy                2
    	-- = 2x  if  y = x
    If you try that, remember to tell the browser to use a fixed-width font in that region. Some of you may also wish to experiment with methods for including graphical images.

    Let's talk about some more detailed ways to access newsgroups from sites around campus.

    Here's the procedure on PC's.

  • Open up Internet Explorer by clicking on the icon with an e in it in the taskbar, lower left part of the screen. Then enter in the Address box, getting to my home page. Then click on the link for math 120, then click on the link for the newsgroup. At this point, internet explorer will start up netscape for you, and the newsgroup will be visible. If you want to start up netscape directly, instead of Internet Explorer, click on the "Start" icon in the lower left corner, click on "Network Services" in the menu, and then click on "Netscape 4.77" in that menu.
  • Here's the procedure for accessing newsgroups from a Macintosh in the computer labs.
  • Locate the folder MAC_APPS in the upper right hand corner of the screen and double click on it to open it. Inside it you will see a folder called "Network Services": open it the same way. Inside that you will see an icon for "Netscape Communicator", a program. Open it the same way. Enter into the Location box to get to my home page. Click on the link for Math 120 this semester. Click on the link for the newsgroup.
  • Here is the procedure for getting Outlook Express to look at newsgroups.
  • Go to to "Tools" then "Accounts" then hit the "Add -> News" button. After that, fill in the correct news server name, and it will walk you through everything else. Then, once the group is shown on the left side, you click on it, and hit the "subscribe" button, and pick the ones you want to subscribe to.
  • Email:

    My email address is Send me some introductory email telling me about yourself, once you get the hang of the email system here. I always reply to email.

    If you have a question about a homework problem, I prefer it to be posted to the news group so my teaching assistants can answer it, and so the other students can benefit from the answer.


    We will cover the following sections of the book: the preview, chapter 1 (except for section 4), chapter 2 (except for section 4), chapter 3, chapter 4 (except for section 6), chapter 5, chapter 6 (except for section 3), chapter 8 (section 3 only).


    It is important to do the homework so you can learn the material and do well on the exams, which will draw material substantially from the homework.

    Homework is collected every Tuesday and Thursday at the beginning of the discussion period, and is marked by your discussion leader. It may happen that more solutions are submitted than can be marked in the time allotted, in which case we will mark just some of them.

    One thing I especially like about the book is the sections called "Applications Plus" and "Problems Plus". The problems in these sections demand extra creativity and extra time spent thinking about it. Please don't get discouraged when you encounter a problem like this and you don't know the method for solving it immediately. We'll discuss problem solving techniques in class that ought to apply to this type of problem.

    Tricky problems:

    Some students complain that math courses contain tricky problems put there just to weed out the weaker students, and not for any useful pedagogical purpose.

    This is not true. Doing homework problems is a lot like lifting weights - you have to do it a lot to get strong. We want you to be strong at solving problems and thinking about mathematics.

    Mathematical theory:

    Some students complain that there is too much emphasis on theory in math courses, and that math professors spend too much time explaining the ideas and not enough time teaching how to execute the algorithms.

    If it were possible for you to live in this world and be successful at your chosen career by following a simple algorithm we would teach you that algorithm. Life today demands a broad set of adaptible skills, and a solid intellectual understanding of science and mathematics is one of them.

    Think about those algorithms - do you want to spend all of your time studying to do something that computers can already do so well? Will that skill be valuable to your future employer? In real life, the problems aren't like homework problems. For example, suppose the problem you confront is to design a way of encoding sound on a CD to render it more resistant to scratches. Are you going to find the answer to that in a textbook? Or will you have developed ways of thinking about problems that will allow you to invent something new and better than what came before?


    There will be frequent quizzes administered in the discussion sections.


    Here is the University's academic calendar. There will be three 1 hour exams in class and a 3 hour final exam, on the following dates.

  • Exam 1: Friday, September 21, 1 PM; brief study guide; answers: 1, 2, 3, 4, 5. The scores were The grading scale was A 85-100, B 74-84, C 60-73, D 50-59. The new grading scale (as of Nov 30) is A 80-100, B 67-79, C 59-66, D 50-58.
  • Exam 2: Wednesday, October 17, 1 PM; brief study guide and answers. The scores were The grading scale was A 77-100, B 65-76, C 50-64, D 40-49.
  • Exam 3: Wednesday, November 14, 1 PM; brief study guide and answers. The scores were The grading scale was A 87-100, B 72-86, C 56-71, D 44-55.
  • Final exam: Monday, December 10, 1:30-4:30 PM; brief study guide. (The schedule for final exams is in the timetable, and there will be no conflict exam.) The scores were
  • Grading policy:

    We will use a scoring scheme where 90% or better is an A, 80-90% is a B, 70-80% is a C, 60-70% is a D, and 0-60% is an F. We will average your scores so that

  • the quizzes count for 8% of your final grade, with the lowest score dropped
  • the homework counts for 8%, with the lowest score dropped
  • the three hour exams each count for 17%, and
  • the final exam counts for 33%.
  • If some calamity that may affect your performance befalls you or your family during the semester, let me know about it right away.

    Appeals about scoring:

    You are welcome to appeal a score which you think was assigned incorrectly. We try our best to score correctly.

    My schedule:

    Office times: Mondays, 2pm, and Wednesdays, 4pm.

    Homework assignments:

  • Thursday, Aug 23: 1.1: 5-8, 14, 16, 30, 32, 34, 36, 60, 62; answers: A, B.
  • Tuesday, Aug 28: 1.2: 2, 4, 14; 1.3: 4, 6, 28, 36, 38, 40, 42, 46, 48. answers: A, B.
  • Thursday, Aug 30: 1.5: 2, 8, 10, 12, 16, 18, 23; 1.6: 1, 2, 14, 22, 24, 28, 32, 57. answers: A, B.
  • Tuesday, Sep 4: p. 83: 10, 11, 12, 14, 17; 2.1: 2, 4, 6. answers: A.
  • Thursday, Sep 6: 2.2: 2, 4, 6, 8, 14, 22, 26, 28. answers: A.
  • Tuesday, Sep 11: 2.7: 2, 8, 10, 16, 20, 22, 26; 2.8: 2, 4, 20, 22, 28, 30, 32. answers: A, B.
  • Thursday, Sep 13: 2.9: 2, 4, 6, 8, 10, 12, 14, 16, 20, 42. answers: A, B.
  • Review questions, not to be turned in: p. 75-77: concepts, quiz, review; p. 174: concepts: 1, 4, 5, 8-12; p. 176: 37-56.
  • Thursday, Sep 20, Problems Plus for Chapter 2, challenging problems, partially or mostly extra credit: p. 178-9: 1, 2, 4, 6, 8, 9, 10, 11. Full explanations needed. Fun and educational.
  • Tuesday, Sep 25: 3.1: 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28; answers.
  • Thursday, Sep 27: 3.1: 44, 48, 61; 3.2: 4, 6, 8, 10, 14, 18, 20, 22, 24, 26, 32, 36, 40. answers.
  • Tuesday, Oct 2: 3.3: 8, 10, 12, 26, 32. 3.4: 2, 4, 6, 8, 10, 12, 18, 22, 38, 40. answers.
  • Thursday, Oct 4: 3.5: 2 - 24 even numbers only. answers.
  • Tuesday, Oct 9: 3.5: 38, 40, 42, 58. 3.6: 6, 10, 14, 18, 28, 30, 32, 38. 3.7: 2, 4, 6, 8, 44, 50. 3.8: 2-16 even numbers only. answers, but careful: the solution here to #42 is completely wrong; the correct solution is (ln 2)(2^3^x^2)(ln 3)(3^x^2)(2 x).
  • Thursday, Oct 11: 3.9: 2, 4, 8, 16, 24, 26, 30-40 even numbers only.
  • Review questions, not to be turned in: p. 267-270: concepts: all problems; quiz: all problems; exercises: 1-90.
  • Thursday, Oct 18, Problems Plus for Chapter 3, challenging problems, mostly extra credit, chapter 3: p. 271-5, 1, 4, 6, 7, 9, 15, 16, 17, 23, 25.
  • Tuesday, Oct 23, 3.10: 5, 6; 3.11: 6, 8, 32, 34, 36, 38, 46; 4.1: 4, 6, 12, 14, 18, 20, 32, 50, 52, 54; answers.
  • Thursday, Oct 25, 3.10: 7, 8, 30, 32; 4.1: 62, 64; 4.3: 2, 4, 6, 7, 8, 32-40 even numbers only, 58; answers; answer sheet also available at the DupIt Copy Shop at 808 S. 6th Street,
  • Tuesday, Oct 30, 4.4: 2, 10, 12, 14, 42, 50. 4.5: 2, 4, 6, 8, 10, 16; 4.7: 2, 4, 6, 8; answers; answer sheet also available at the DupIt Copy Shop at 808 S. 6th Street.
  • Thursday, Nov 1, (due date postponed until Nov 2 at 3pm in your TA's mailbox, room 250 Altgeld) 4.7: 10, 18, 30, 40, 48, 50, 52, 54, 56; answers.
  • Tuesday, Nov 6, 4.8: 2, 4, 14, 16 (originally due on Thursday Nov.1); 4.9: 2, 6, 12; 4.10: 2, 8, 12, 26; 5.1: 4, 12; 5.2: 6, 10, 30, 32, 34, 36; answer sheet available at the DupIt Copy Shop at 808 S. 6th Street.
  • Friday, Nov 9, at 3pm (originally due on Thursday), 5.3: 2, 6, 8, 18-38 even numbers only; answers: part a, part b.
  • Review questions for exam 3, not to be turned in: Chapter 3, p. 267-270: concept check: 6a; exercises: 91-97; Chapter 4, p. 359-362: concept check: all, except the ones beginning with "State the"; quiz: all; exercises: all [except #47, the ones marked CAS, and the ones marked with a graphing calculator screen]; Chapter 5, p. 425-428: concept check: 1-3; quiz: all; exercises: 1-24.
  • Friday, Nov 16, 3pm, in your TA's mailbox, room 250 Altgeld, Problems Plus for Chapter 4, challenging problems, mostly extra credit, pages 363-365: 2, 4, 6, 10, 12, 17, 20, 22, 24.
  • Tuesday, Nov 27, 5.4: 6, 8, 10, 46, 48, 50; 5.5: 6-14 even numbers only, 50-58 even numbers only; answers.
  • Thursday, Nov 29, 5.5: 62, 64, 66; 6.1: 2, 4, 8, 18, 22, 28; answers.
  • Friday, Nov 30, 3pm, in your TA's mailbox, room 250 Altgeld, Problems Plus for Chapter 5, challenging problems, mostly extra credit, pages 429-431: 14, 16, 20 (18 points).
  • Tuesday, Dec 4, 6.2: 2, 4, 6, 8, 44, 52, 54, 66; 6.4: 2, 6, 10, 12, 16; 6.5: 2, 4, 6; answers.